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Lecture Notes

Note: Reduced means 4 viewgraphs per page. Full size is one per page.
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• Set number 14 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Dec 9 07:48:49 CST 2020
  Topics: [Last set of notes] Large Sparse eigenvalue problems; Rayleigh-Ritz projection; Subspace iteration; Lanczos algorithms; Loss of orthogonality; Golub-Kahan-Lanczos bidiagonalization.
      Supplement: Solutions to exercises and more. PDF    

• Set number 13 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Dec 3 09:59:54 CST 2020
  Topics: Eigenvalue problems (continued); The QR algorithm; Practical variants; Symmetric eigenvalue problems -Min-max theorem; The law of intertia; The QR algorithm for symmetric matrices; The Jacobi algorithm.
      Supplement: Solutions to exercises and more. PDF    

• Set number 12 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Nov 23 11:34:25 CST 2020
  Topics: Eigenvalue problems; Brief background; the Schur form; Perturbation analysis; conditioning of a simple eigenvalues; The power method and related techniques.
      Supplement: Solutions to exercises and more. PDF    

• Set number 11 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Nov 22 14:49:00 CST 2020
  Topics: A few applications of the SVD; Regularization; Information retrieval; Principal Component Analysis (PCA); Dimension reduction.
      Supplement: Solutions to exercises and more. PDF    

• Set number 10 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Nov 15 10:54:57 CST 2020
  Topics: The Pseudo inverse; Application to least-squares; Moore-Penrose Pseudo-in Ill-conditioned systems and the SVD; Numerical rank and the SVD;
      Supplement: Solutions to exercises and more. PDF    

• Set number 9 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Nov 3 15:14:06 CST 2020
  Topics: Orthogonal subspaces & orthogonal projectors; Orthogonal decomposition; The 4 fundamental subspaces; the URV decomposition. Introduction to the Singular Value Decomposition. The singular value decomposition and its properties.
      Supplement: Solutions to exercises and more. PDF    

• Set number 8 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Nov 1 17:31:37 CST 2020
  Topics: The Householder QR; the rank Deficient case; Computational cost; Solving Least-squares problems with the householder QR; Givens rotations and the Givens QR.
      Supplement: Solutions to exercises and more. PDF    

• Set number 7 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Oct 22 08:09:02 CDT 2020
  Topics: The Gram-Schmidt algorithms and the QR Factorization; Least-squares problems; Applications; Data fitting;
      Supplement: Solutions to exercises and more. PDF    

• Set number 6 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Oct 18 14:52:11 CDT 2020 [reposted with minor changes -- 11/03/20]
  Topics: Positive Definiteness; Symmetric Positive Matrices; The LDLT and Cholesky factorizations.
      Supplement: Solutions to exercises and more. PDF    

• Set number 5 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Oct 11 12:53:05 CDT 2020
  Topics: Perturbation theory for linear systems; sensitivity analysis; Condition numbers; Error bounds; Norm-wise error analysis; Estimating cond. numbers; Estimating forward errors from residual norms.
      Supplement: Solutions to exercises and more. PDF    

• Set number 4 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Oct 4 16:38:05 CDT 2020
  Topics: Concepts in floating point arithmetic; Error analysis Forward and backward errors; Errors in inner products; Application to linear systems.
      Supplement: Solutions to exercises and more. PDF    

• Set number 3 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Sep 22 16:51:49 CDT 2020
  Topics: Solving Linear Systems; Background; Gaussian Elimination (review); Gauss-Jordan; The LU factorization; Pivoting.
      Supplement: Solutions to exercises and more. PDF    

• Set number 2 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Sep 15 10:09:04 CDT 2020
  Topics: Inner products and norms; Vector norms; Convergence of vector sequences; Matrix norms.
      Supplement: Solutions to exercises and more. PDF    

• Set number 1 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Sep 7 12:35:18 CDT 2020
  Topics: Introduction; Types of problems seen in this course ; Math. background; Matrices; Eigenvalues and eigenvectors; Null space and range; Rank; Types of matrices; Special matrices.
      Supplement: Solutions to exercises and more. PDF    

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csci 5304 - Fall 2020